| Relation among C-curve characterization diagrams |
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| 作者姓名： | CAO Juan WANG Guo-zhao |
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| 作者单位： | Institute of Computer Graphics and Image Processing，Department of Mathematics，Zhejiang University，Hangzhou 310027，China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China （No. 60473130） and the National Basic Research Program （973） of China （No. 2004CB318000） |
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| 摘 要： | As three control points are fixed and the fourth control point varies, the planar cubic C-curve may take on a loop, a cusp, or zero to two inflection points, depending on the position of the moving point. The plane can, therefore, be partitioned into regions labelled according to the characterization of the curve when the fourth point is in each region. This partitioned plane is called a "characterization diagram". By moving one of the control points but fixing the rest, one can induce different characterization diagrams. In this paper, we investigate the relation among all different characterization diagrams of cubic C-curves based on the singularity conditions proposed by Yang and Wang (2004). We conclude that, no matter what the C-curve type is or which control point varies, the characterization diagrams can be obtained by cutting a common 3D characterization space with a corresponding plane.
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| 关 键 词： | 样条 C曲线 特征图表 奇点 |
| 收稿时间： | 2007-01-25 |
| 修稿时间： | 2007-04-03 |
Relation among C-curve characterization diagrams |
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| CAO Juan WANG Guo-zhao.Relation among C-curve characterization diagrams[J].Journal of Zhejiang University Science,2007,8(10):1663-1670. |
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| Authors: | Cao Juan Wang Guo-zhao |
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| Institution: | (1) Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | As three control points are fixed and the fourth control point varies, the planar cubic C-curve may take on a loop, a cusp, or zero to two inflection points, depending on the position of the moving point. The plane can, therefore, be partitioned into regions labelled according to the characterization of the curve when the fourth point is in each region. This partitioned plane is called a "characterization diagram". By moving one of the control points but fixing the rest, one can induce different characterization diagrams. In this paper, we investigate the relation among all different characterization diagrams of cubic C-curves based on the singularity conditions proposed by Yang and Wang (2004). We conclude that, no matter what the C-curve type is or which control point varies, the characterization diagrams can be obtained by cutting a common 3D characterization space with a corresponding plane. |
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| Keywords: | Spline C-curve Characterization diagram Singularity |
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